The Center for American Progress has released a study in which they attempt to claim that immigration attrition (see the link) doesn't work. What they do instead is unwittingly admit that it does work, it just needs to be nationwide.

Leah Muse-Orlinoff [1] offers "Staying Put but Still in the Shadows: Undocumented Immigrants Remain in the Country Despite Strict Laws" [1]:

With more than 11 million unauthorized immigrants currently living in the country, a consensus has emerged that the current immigration system is broken and badly needs mending. In the absence of federal legislation providing a coherent immigration policy, states have taken it upon themselves to enforce their way to a solution. Arizona, Georgia, and Alabama recently took matters into their own hands by passing laws designed to criminalize virtually all activity engaged in by undocumented immigrants. This patchwork of state and local laws is driven by a strategy known by immigration restrictionists as “attrition through enforcement.” The goal is to create a climate of fear and make life so difficult for immigrants that they will self-deport...

...we find that:

1. Most unauthorized immigrants make the decision to stay in the country despite attempts to drive them out. The proliferation of state-level anti- immigrant laws has not changed the calculus for immigrants when it comes to choosing to stay here or return home.

2. At best, anti-immigrant laws simply drive immigrants from one area to another—say from one county to the next, or from one state to the next— rather than from the country. At worst, they further isolate immigrants from the communities they live in and from local law enforcement, while driving families deeper into the shadows.

In other words, attrition does work for those localities that try it: illegal aliens leave of their own accord. Illegal aliens pick up and leave for more welcoming destinations. It stands to reason that if attrition were a nationwide program - and not just restricted to some states or cities - illegal aliens would decide to leave the U.S. for their home countries. Those who want to profit from illegal immigration in one way or another will say different, but this study isn't going to help them: it shows that illegal aliens do make the rational decision to leave areas that don't support illegal immigration. The only way to be sure would be to try attrition on a nationwide basis for a few years and see what happens, which is the last thing illegal immigration supporters want: they know it would work. That's why they fight so hard against laws like those in Arizona.